I cannot overemphasize how important it is to critically
assess the worth of the hypotheses being tested within any study based
upon a two-way ANOVA. No matter how good the study may be from a statistical
perspective and no matter how clear the research report is, the study
cannot possibly make a contribution unless the questions being dealt
with are interesting. In other words, the research questions that prompt the
investigator to select the factors and levels of the two-way ANOVA must
be worth answering and must have no clear answer before the study is
conducted. If these things do not hold true, then the study has a fatal
flaw in its foundation that cannot be overcome by appropriate sample sizes, rigorous alpha
levels, high reliability and validity estimates, impressive F-ratios
that are statistically significant, tests of assumptions, Bonferroni corrections, F-ratios
that are statistically significant, and elaborate post hoc analyses. The old saying that
"You can't make a silk purse from a sow's ear" is as relevant here as anywhere
else.